ICA  Vol.5 No.1 , February 2014
Hierarchical Structure of Multicriteria Problems
ABSTRACT

It is shown that any multicriteria problem can be represented by a hierarchical system of criteria. Individual properties of the object (alternative) are evaluated at the bottom level of the system, using a criteria vector. A composition mechanism is used to evaluate the object as a whole at the top level. The problem is solved by the method of nested scalar convolutions of vector-valued criteria. The methodology of the problem solving is based on the complementarity principle by N. Bohr and the theorem of incompleteness by K. G?del. An example is presented that helps the reader digest some of the intricacies in the methodology.


Cite this paper
Voronin, A. and Ziatdinov, Y. (2014) Hierarchical Structure of Multicriteria Problems. Intelligent Control and Automation, 5, 12-18. doi: 10.4236/ica.2014.51002.
References
[1]   V. A. Gubanov, V. V. Zakharov and A. N. Kovalenko, “Introduction to Systems Analysis,” [in Russian], Leningrad State University, Leningrad, 1988.

[2]   A. N. Voronin, Ju. K. Ziatdinov and M. V. Kuklinsky, “Multicriteria Decisions: Models and Methods,” [in Russian], NAU, Kiev, 2011.

[3]   P. Fishburne, “Utility Theory for Decision Making,” [in Russian], Nauka, Moscow City, 1978.

[4]   T. L. Saaty, “Multicriteria Decision Making: The Analytical Hierarchy Process,” McGraw-Hill, New York, 1990.

[5]   A. N. Voronin, “The Method of Multicriteria Evaluation and Optimization of Hierarchical Systems,” [in Russian], Cybernetics and Systems Analysis, No. 3, 2007, pp. 84-92.

 
 
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